#64480⋊C₂ #10597170

order	600
isoclinism	isoclinic class of #64480⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	#64480⋊C₂
unambiguous semidirect product	(#1043⋊C₃)⋊C₂

Fitting, socle, Sylow	C₅² ⋊ C₄×D₃
derived, Hall	C₅²⋊C₃ ⋊ C₂×C₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₅²⋊C₃	C₂×C₄
Fitting, socle	C₅²	C₄×D₃
prime radical	#3874⋊C₂	C₂
cosocle	(C₅⋊D₅)⋊C₃	C₂²
LCS	G ▷ C₅²⋊C₃
UCS	C₁

48 conjugacy classes of subgroups.

μ_t(G) = 15

Polycyclic presentation:

2^3,3,5^2|a^2=c,e^a=e^3,f^a=f^3,d^b=d^2,f^b=e^4f^4,e^c=e^4,f^c=f^4,e^d=ef^3,f^d=e^4f^3

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 151);